stokes_taylor_error_dg.cc

The Stokes problem for the Taylor benchmark by the discontinuous Galerkin method – error analysis

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "taylor_exact.h"
int main(int argc, char**argv) {
environment rheolef(argc, argv);
Float err_linf_expected = (argc > 1) ? atof(argv[1]) : 1e+38;
bool dump = (argc > 2);
field uh;
din >> uh;
space Xh = uh.get_space();
geo omega = Xh.get_geo();
space Qh (omega, Xh.get_approx());
field ph(Qh);
din >> ph;
size_t k = Xh.degree();
size_t d = omega.dimension();
integrate_option iopt;
iopt.set_family(integrate_option::gauss);
iopt.set_order(2*k+1);
Float meas_omega = integrate (omega);
Float moy_ph = integrate (omega, ph, iopt);
ph = ph - moy_ph/meas_omega; // ph with zero average value
string high_approx = "P"+itos(k+1)+"d";
space Xh1 (omega, high_approx, "vector"),
Qh1 (omega, high_approx);
field euh = interpolate (Xh1, uh-u_exact());
field eph = interpolate (Qh1, ph-p_exact());
Float err_u_l2 = sqrt(integrate (omega, norm2(uh-u_exact()), iopt));
Float err_u_linf = euh.max_abs();
Float err_u_h1 = sqrt(integrate (omega, norm2(grad_h(euh)), iopt)
+ integrate (omega.sides(), (1/h_local())*norm2(jump(euh)), iopt));
Float err_p_l2 = sqrt(integrate (omega, sqr(ph-p_exact()), iopt));
Float err_p_linf = eph.max_abs();
derr << "err_u_l2 = " << err_u_l2 << endl
<< "err_u_linf = " << err_u_linf << endl
<< "err_u_h1 = " << err_u_h1 << endl
<< "err_p_l2 = " << err_p_l2 << endl
<< "err_p_linf = " << err_p_linf << endl;
if (dump) {
dout << catchmark("uh") << uh
<< catchmark("u") << interpolate (Xh, u_exact())
<< catchmark("eu") << euh
<< catchmark("ph") << ph
<< catchmark("p") << interpolate (Qh, p_exact())
<< catchmark("ep") << eph;
}
return (max(err_u_linf,err_p_linf) <= err_linf_expected) ? 0 : 1;
}
Float
see the Float page for the full documentation
field
see the field page for the full documentation
geo
see the geo page for the full documentation
rheolef::integrate_option::gauss
@ gauss
Definition: integrate_option.h:132
rheolef::din
idiststream din
see the diststream page for the full documentation
Definition: diststream.h:427
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
rheolef::derr
odiststream derr(cerr)
see the diststream page for the full documentation
Definition: diststream.h:436
space
see the space page for the full documentation
dump
verbose clean transpose logscale grid shrink ball stereo iso volume skipvtk deformation fastfieldload lattice reader_on_stdin color format format format format format format format format format format format format format format format format format format dump
Definition: iorheo-members.h:119
mkgeo_ball.d
int d
Definition: mkgeo_ball.sh:154
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::h_local
details::field_expr_v2_nonlinear_terminal_function< details::h_local_pseudo_function< Float > > h_local()
h_local: see the expression page for the full documentation
Definition: field_expr_terminal.h:527
rheolef::grad_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:949
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
rheolef::interpolate
field_basic< T, M > interpolate(const space_basic< T, M > &V2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: interpolate.cc:233
rheolef::norm2
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition: vec.h:379
rheolef::itos
std::string itos(std::string::size_type i)
itos: see the rheostream page for the full documentation
rheolef.h
rheolef - reference manual
main
int main(int argc, char **argv)
Definition: stokes_taylor_error_dg.cc:29
p_exact
Definition: taylor_exact.h:27
taylor_exact.h
The Taylor benchmark – the exact solution of the Stokes problem.
u_exact
g u_exact
Definition: taylor_exact.h:26